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Single Idea 9517
[filed under theme 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
]
Full Idea
The 'scope' of a connective in a certain formula is the formulae linked by the connective, together with the connective itself and the (theoretically) encircling brackets
Clarification
'Theoretically' because logicians leave out brackets if they are unimportant
Gist of Idea
The 'scope' of a connective is the connective, the linked formulae, and the brackets
Source
E.J. Lemmon (Beginning Logic [1965], 2.1)
Book Ref
Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.47
The
16 ideas
with the same theme
[definitions of the main concepts in propositional logic]:
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9517
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The 'scope' of a connective is the connective, the linked formulae, and the brackets
[Lemmon]
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9516
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A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔
[Lemmon]
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9518
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A 'theorem' is the conclusion of a provable sequent with zero assumptions
[Lemmon]
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9519
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A 'substitution-instance' is a wff formed by consistent replacing variables with wffs
[Lemmon]
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9529
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A wff is 'inconsistent' if all assignments to variables result in the value F
[Lemmon]
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9531
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'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology
[Lemmon]
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9534
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Two propositions are 'equivalent' if they mirror one another's truth-value
[Lemmon]
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9530
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A wff is 'contingent' if produces at least one T and at least one F
[Lemmon]
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9532
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'Subcontrary' propositions are never both false, so that A∨B is a tautology
[Lemmon]
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9533
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A 'implies' B if B is true whenever A is true (so that A→B is tautologous)
[Lemmon]
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9528
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A wff is a 'tautology' if all assignments to variables result in the value T
[Lemmon]
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9540
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A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0
[Hughes/Cresswell]
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13422
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'Conjunctive Normal Form' is ensuring that no disjunction has a conjunction within its scope
[Bostock]
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13421
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'Disjunctive Normal Form' is ensuring that no conjunction has a disjunction within its scope
[Bostock]
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13689
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'Theorems' are formulas provable from no premises at all
[Sider]
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13520
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A 'tautology' must include connectives
[Wolf,RS]
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